My professor assigned a completely random question on our problem set. Basically, it goes:
Sophie is 30 years old and majored in philosophy. As a student, she participated in anti-nuclear demonstrations and was deeply concerned with social justice. Which is more probable?
1. Sophie is a bank teller.
2. Sophie is a bank teller and is active in the feminist movement.
I'm guessing the point the prof was trying to get across is that assuming you have two different events $A$ and $B$, $A\cap B$ would always have a smaller probability than either. Is this correct?